: The broad, long-term objectives of this research are the development of non- and semi-parametric statistical methods for analyzing censored data often encountered in biomedical investigations. In the next project period, major efforts will be directed at two timely and important areas in which there are substantial gaps of knowledge: interval censored and multivariate failure time data. Interval censored data arise when the failure time of interest is only known to lie in a random interval while multivariate failure time data arise when each subject may experience several events or when there is clustering of subjects which induces dependence among failure times of the same cluster. These two types of data are commonly encountered in the clinical and epidemiological studies of many diseases, and have arisen with greater frequencies in recent years especially in disease prevention trials and HIV/AIDS research. Although considerable recent efforts have been made on these two difficult topics, there still lack satisfactory solutions to several important problems, some of which will be studied in this project. Specifically, this research will develop simple nonparametric test statistics to compare failure time distributions as well as semiparametric additive hazards regression methods to estimate covariate regression for the gap time distributions of serial events subject to right censoring, and explore a new class of semiparametric frailty and marginal regression models for multivariate failure times which can be easily analyzed under both right- and interval- censorship. Although these problems are highly challenging, requiring fresh ideas and innovative techniques, preliminary investigations have shown considerable promise for simple and elegant solutions. The asymptotic properties of the proposed estimators and test statistics will be rigorously studied with the use of counting-process martingale theory, modern empirical process theory and other probability tools, and their operating characteristics investigated through extensive simulations. All the proposed methods will be implemented in computer programs for public use and applied to real biomedical studies.